{"id":1413,"date":"2024-08-28T18:10:38","date_gmt":"2024-08-28T18:10:38","guid":{"rendered":"https:\/\/sites.wcsu.edu\/roccac\/?page_id=1413"},"modified":"2026-10-07T21:36:18","modified_gmt":"2026-10-07T21:36:18","slug":"multivariable-math-for-machine-learning","status":"publish","type":"page","link":"https:\/\/sites.wcsu.edu\/roccac\/homepage\/multivariable-math-for-machine-learning\/","title":{"rendered":"Multivariable Math for Machine Learning"},"content":{"rendered":"\n<h1 class=\"wp-block-heading has-text-color has-link-color wp-elements-e69fe90a0f56debb7f83920e84056666\" style=\"color:#002856\"><strong><a href=\"https:\/\/sites.wcsu.edu\/roccac\/wp-content\/uploads\/sites\/33\/2026\/09\/2026_Fall_MAT_531_Syllabus.pdf\">Syllabus<\/a><\/strong><\/h1>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\" \/>\n\n\n\n<h1 class=\"wp-block-heading\">Texts<\/h1>\n\n\n\n<p>This semester we will be using a linear algebra text for the majority of the semester but will supplement with material from other texts.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Primary Text: &#8220;Linear Algebra and it&#8217;s Applications 6th ed.&#8221; by Lay, Lay, and McDonald (A PDF of the fifth edition can be found online and has most of the same content.  I have also placed a physical copy of the fifth edition on reserve in the library.) Chapters 4-7 and some of 10<\/li>\n\n\n\n<li>Supplementary Text:<a href=\"https:\/\/mml-book.github.io\/book\/mml-book.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"> &#8220;Mathematics for Machine Learning&#8221; by Deisenroth, Faisl, and Ong<\/a>, Chapters 1-5 and 7<\/li>\n\n\n\n<li>Supplementary Text: <a href=\"https:\/\/openstax.org\/details\/books\/calculus-volume-3\" target=\"_blank\" rel=\"noreferrer noopener\">&#8220;Calculus Volume 3&#8221; from OpenStax<\/a>, Chapters  2-4<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\" \/>\n\n\n\n<h1 class=\"wp-block-heading has-text-color has-link-color wp-elements-c9a1a8ad8d28649de8bb975357fb415d\" style=\"color:#002856\">Calendar<\/h1>\n\n\n\n<p>There is a proposed calendar on the syllabus, but here I will record what we actually get through in each class.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>&#8230;<\/li>\n\n\n\n<li>10\/7\/2026: Exam 1 on Linear Algebra Basics<\/li>\n\n\n\n<li>9\/30\/2026: The exam is next week, we will start class answering questions, but we can&#8217;t spend too much time on it because you need time to complete the exam. <strong><span style=\"text-decoration: underline\"><em>Review the material from the four sets of review slides<\/em><\/span><\/strong> which review the basic prerequisite linear algebra from a first course in linear algebra. In particular review your notes and the review slides and come in ready to demonstrate knowledge of the following review topics (Chapters\/Sections refer to the 5th Edition of Lay&#8217;s Linear Algebra text that, as I have previously pointed out, is on reserve in the library and can probably be found online as a pdf):\n<ul class=\"wp-block-list\">\n<li>Basic matrix, vector, and scalar arithmetic (Section 2.1),<\/li>\n\n\n\n<li>Finding solutions to systems of equations by row reducing augmented matrices (Section 1.1-1.5),<\/li>\n\n\n\n<li>Calculating dot products and using them to find the norm of a vector or the projection of one vector onto another (Section 6.1 and 6.2),<\/li>\n\n\n\n<li>Finding the determinant of a matrix and explaining the significance of that determinant (Chapter 3),<\/li>\n\n\n\n<li>Identifying if a set of vectors are linearly independent (Section 1.7, 4.3),<\/li>\n\n\n\n<li>Identifying the span of a set of vectors (Section 1.3),<\/li>\n\n\n\n<li>Identifying if a set of vectors is a basis for \\(\\mathbb{R}^n\\) for \\(n=2,3\\) (Section 4.3 and 4.4),<\/li>\n\n\n\n<li>Finding the change of basis matrix between two bases (Section 4.7),<\/li>\n\n\n\n<li>Finding the eigenvalues and eigenvectors of a \\(2\\times 2\\) or \\(3\\times 3\\) matrix (Sections 5.1 and 5.2),<\/li>\n\n\n\n<li>Diagonalizing a \\(2\\times 2\\) or \\(3\\times 3\\) matrix (Section 5.3).<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>9\/23\/2026: We reviewed previous topics and covered most of the key material from the fourth set of review slides. We will do some review next week and have the exam on the <em>Review of Linear Algebra<\/em> on October 7th. Please carefully review the material from the four sets of review slides which review the basic prerequisite linear algebra from a first course in linear algebra. In particular review your notes and the review slides and come in ready to demonstrate knowledge of the following review topics:\n<ul class=\"wp-block-list\">\n<li>Basic matrix, vector, and scalar arithmetic,<\/li>\n\n\n\n<li>Finding solutions to systems of equations by row reducing augmented matrices,<\/li>\n\n\n\n<li>Calculating dot products and using them to find the norm of a vector or the projection of one vector onto another,<\/li>\n\n\n\n<li>Finding the determinant of a matrix and explaining the significance of that determinant,<\/li>\n\n\n\n<li>Identifying if a set of vectors are linearly independent,<\/li>\n\n\n\n<li>Identifying the span of a set of vectors,<\/li>\n\n\n\n<li>Identifying if a set of vectors is a basis for \\(\\mathbb{R}^n\\) for \\(n=2,3\\),<\/li>\n\n\n\n<li>Finding the change of basis matrix between two bases,<\/li>\n\n\n\n<li>Finding the eigenvalues and eigenvectors of a \\(2\\times 2\\) or \\(3\\times 3\\) matrix,<\/li>\n\n\n\n<li>Diagonalizing a \\(2\\times 2\\) or \\(3\\times 3\\) matrix.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>9\/16\/2026: We went over the slides on GitHub and Code Spaces, looked through the Jupyter Notebook introduction linear algebra operations in Python, and then went through the third Review of Linear Algebra slide deck.  We will finish the review next week and have the Unit 1 exam the week after.  Please be sure to review the slide decks and your notes.<\/li>\n\n\n\n<li>9\/9\/2026: We started class by reviewing the material we covered the previous week. We will do the same thing next week, please review your notes so that it goes more smoothly. We thne worked through the second set of review slides. Next week, after review, we will look at how we will be using GitHub in this class, please create a personal fork of the repository for the class <a href=\"https:\/\/github.com\/cfroccajr\/Mathematics-for-Machine-Learning.git\" data-type=\"link\" data-id=\"https:\/\/github.com\/cfroccajr\/Mathematics-for-Machine-Learning.git\" target=\"_blank\" rel=\"noreferrer noopener\">Link to Class Repository: https:\/\/github.com\/cfroccajr\/Mathematics-for-Machine-Learning.git<\/a>. Here is a slide deck introducing some basics of what we will be looking at next week: <a href=\"https:\/\/sites.wcsu.edu\/roccac\/wp-content\/uploads\/sites\/33\/2026\/09\/Github_Codespace_Beamer_Presentation___MMML.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">GitHub and Code Spaces Slide Deck Link<\/a><\/li>\n\n\n\n<li>9\/2\/2026: We covered the syllabus and the material in the first set of slides. We will look at the second set of slides and Github\/Jupyter notebooks next time.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\" \/>\n\n\n\n<h1 class=\"wp-block-heading has-text-color has-link-color wp-elements-adde027eeeaf6fc24779a0692c45d201\" style=\"color:#002856\">Assignments:<\/h1>\n\n\n\n<p>Material for assignments will be pulled from the text books, from some projects that go along with Lay&#8217;s text (<a href=\"http:\/\/bit.ly\/30IM8gT\" data-type=\"link\" data-id=\"bit.ly\/30IM8gT\" target=\"_blank\" rel=\"noreferrer noopener\">projects from Lay are at bit.ly\/30IM8gT<\/a>)<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Miscellaneous:<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Get setup on GitHub: Fork the class repository, Create a folder with your last name in the submissions folder, Create a Markdown readme file in the folder you just created (content isn&#8217;t important we&#8217;re just making sure you can complete the work), and create a pull request back to the original class repository as a way of submitting your work.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Projects:<\/h2>\n\n\n\n<p>Most of the the following projects are based on material in Lay&#8217;s Linear Algebra.  As the semester progresses I will post Jupyter notebooks to GitHub to help get started on each project.  Specifically they will give useful Python commands for carrying out the projects and some extensions of the projects.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><a href=\"https:\/\/media.pearsoncmg.com\/aw\/aw_lay_linearalg_updated_cw_5\/student\/applications\/MatLab\/MatLab_pdfs\/ch5\/Fibonacci.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">Fibonacci Like Sequences<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/media.pearsoncmg.com\/aw\/aw_lay_linearalg_6\/projects\/Dynamic.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">Dynamical Systems<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/media.pearsoncmg.com\/aw\/aw_lay_linearalg_6\/projects\/Power.pdf\" data-type=\"link\" data-id=\"https:\/\/media.pearsoncmg.com\/aw\/aw_lay_linearalg_6\/projects\/Power.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">Power Method for Eigenvalues<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/media.pearsoncmg.com\/aw\/aw_lay_linearalg_updated_cw_5\/student\/applications\/MatLab\/MatLab_pdfs\/ch6\/QRMethod.pdf\" data-type=\"link\" data-id=\"https:\/\/media.pearsoncmg.com\/aw\/aw_lay_linearalg_updated_cw_5\/student\/applications\/MatLab\/MatLab_pdfs\/ch6\/QRMethod.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">QR Method for Eigenvalues<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/media.pearsoncmg.com\/aw\/aw_lay_linearalg_updated_cw_5\/student\/applications\/MatLab\/MatLab_pdfs\/ch5\/IntegrationByParts.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">Integration by Parts<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/media.pearsoncmg.com\/aw\/aw_lay_linearalg_updated_cw_5\/student\/applications\/MatLab\/MatLab_pdfs\/ch4\/ErrorCorrectingCodes.pdf\" data-type=\"link\" data-id=\"https:\/\/media.pearsoncmg.com\/aw\/aw_lay_linearalg_updated_cw_5\/student\/applications\/MatLab\/MatLab_pdfs\/ch4\/ErrorCorrectingCodes.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">Error Detecting and Correcting<\/a><\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading\">Text Material<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>&#8230;<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\" \/>\n\n\n\n<h1 class=\"wp-block-heading has-text-color has-link-color wp-elements-b72152fe5634ca5b96961c68b0f1cbae\" style=\"color:#002856\">Previous Semester Lecture Slides<\/h1>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/sites.wcsu.edu\/roccac\/wp-content\/uploads\/sites\/33\/2025\/09\/Review_Vector_and_Matrix_Operations__Part_1____Slides.pdf\" data-type=\"link\" data-id=\"https:\/\/sites.wcsu.edu\/roccac\/wp-content\/uploads\/sites\/33\/2024\/08\/Review_Vector_and_Matrix_Operations_Part_1_Slides.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">Review of Linear Algebra: Matrix and Vector Arithmetic (Fall 2025 Edition)<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/sites.wcsu.edu\/roccac\/wp-content\/uploads\/sites\/33\/2025\/09\/Review_Vector_and_Matrix_Operations__Part_2__Slides.pdf\" data-type=\"link\" data-id=\"https:\/\/sites.wcsu.edu\/roccac\/wp-content\/uploads\/sites\/33\/2024\/08\/Review_Vector_and_Matrix_Operations_Part_2_Slides.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">Review of Linear Algebra: Equations, Inverses, Determinants (Fall 2025 Edition)<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/sites.wcsu.edu\/roccac\/wp-content\/uploads\/sites\/33\/2025\/09\/Bases_and_Coordinates_Slides.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">Review of Linear Algebra: Bases and Coordinates (Fall 2025 Edition)<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/sites.wcsu.edu\/roccac\/wp-content\/uploads\/sites\/33\/2025\/09\/Eigenvalues_and_their_Kin_Slides.pdf\" data-type=\"link\" data-id=\"https:\/\/sites.wcsu.edu\/roccac\/wp-content\/uploads\/sites\/33\/2024\/09\/Eigenvalues_and_their_Kin_Slides.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">Review of Linear Algebra: Eigenvalues and Eigenvectors (Fall 2025 Edition)<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/sites.wcsu.edu\/roccac\/wp-content\/uploads\/sites\/33\/2024\/10\/Inner_Products__Norms__and_Orthogonalization_Slides.pdf\" data-type=\"link\" data-id=\"https:\/\/sites.wcsu.edu\/roccac\/wp-content\/uploads\/sites\/33\/2024\/10\/Inner_Products__Norms__and_Orthogonalization_Slides.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">Orthogonalization, Regression, and Inner Products<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/sites.wcsu.edu\/roccac\/wp-content\/uploads\/sites\/33\/2024\/10\/Symmetric_Matrices__Quadratic_Forms__and_Optimization_Slides.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">Symmetric Matrices and Basic Optimization<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/sites.wcsu.edu\/roccac\/wp-content\/uploads\/sites\/33\/2024\/10\/Symmetric_Matrices_PCA_and_SVD_Slides.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">Symmetric Matrices SVD and PCA<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/sites.wcsu.edu\/roccac\/wp-content\/uploads\/sites\/33\/2025\/11\/Moving_Calculus_to_the_Third_Dimension_Slides__Lines_and_Planes_.pdf\" data-type=\"link\" data-id=\"https:\/\/sites.wcsu.edu\/roccac\/wp-content\/uploads\/sites\/33\/2025\/11\/Moving_Calculus_to_the_Third_Dimension_Slides__Lines_and_Planes_.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">Lines and Plains in Multiple Dimensions<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/sites.wcsu.edu\/roccac\/wp-content\/uploads\/sites\/33\/2025\/11\/Moving_Calculus_to_the_Third_Dimension_Slides__Limits_and_Derivatives_.pdf\" data-type=\"link\" data-id=\"https:\/\/sites.wcsu.edu\/roccac\/wp-content\/uploads\/sites\/33\/2025\/11\/Moving_Calculus_to_the_Third_Dimension_Slides__Limits_and_Derivatives_.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">Limits and Derivatives in Multiple Dimensions<\/a><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\" \/>\n","protected":false},"excerpt":{"rendered":"<p>Syllabus Texts This semester we will be using a linear algebra text for the majority of the semester but will supplement with material from other texts. Calendar There is a proposed calendar on the syllabus, but here I will record &hellip; <a href=\"https:\/\/sites.wcsu.edu\/roccac\/homepage\/multivariable-math-for-machine-learning\/\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":35,"featured_media":0,"parent":2,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"wpo365_audiences":[],"wpo365_private":false,"footnotes":""},"class_list":["post-1413","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sites.wcsu.edu\/roccac\/wp-json\/wp\/v2\/pages\/1413","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.wcsu.edu\/roccac\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sites.wcsu.edu\/roccac\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sites.wcsu.edu\/roccac\/wp-json\/wp\/v2\/users\/35"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.wcsu.edu\/roccac\/wp-json\/wp\/v2\/comments?post=1413"}],"version-history":[{"count":24,"href":"https:\/\/sites.wcsu.edu\/roccac\/wp-json\/wp\/v2\/pages\/1413\/revisions"}],"predecessor-version":[{"id":2372,"href":"https:\/\/sites.wcsu.edu\/roccac\/wp-json\/wp\/v2\/pages\/1413\/revisions\/2372"}],"up":[{"embeddable":true,"href":"https:\/\/sites.wcsu.edu\/roccac\/wp-json\/wp\/v2\/pages\/2"}],"wp:attachment":[{"href":"https:\/\/sites.wcsu.edu\/roccac\/wp-json\/wp\/v2\/media?parent=1413"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}